The ISOC acts as strong effective Zeeman fields, which polarize
electron spins oppositely to the out-of-plane direction at opposite
valleys, that is, at the \(\mathbf {K}\)  and \(-\mathbf {K}\)  points in
Fig. REF (b). If we choose the out-of-plane direction as the
\(z\) -axis, the ISOC term has the form [1]}
\(H_{ISOC}(k)=\beta \sum _{k,\sigma ,\sigma ^{\prime }}\mathbf {g}_{k}\cdot \mathbf {\hat{\sigma }}_{\sigma \sigma ^{\prime }}(a^{\dag }_{k,\sigma }a_{k,\sigma ^{\prime }}+b^{\dag }_{k,\sigma }b_{k,\sigma ^{\prime }}),\) 
